# A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 15 , 12 , and 7 , respectively. What is the rectangle's area?

Apr 19, 2016

63 square units

#### Explanation:

The area of the rectangle attached to B = 7B

Since the triangle is right with hypotenuse A , we can use$\textcolor{b l u e}{\text{ Pythagoras' theorem " " to calculate B }}$

$\Rightarrow {A}^{2} = {B}^{2} + {C}^{2}$

and : ${B}^{2} = {A}^{2} - {C}^{2} = {15}^{2} - {12}^{2} = 81$

now ${B}^{2} = 81 \Rightarrow B = \sqrt{81} = 9$

therefore area of rectangle = 7B =$7 \times 9 = 63 \text{ square units }$